Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
An Open Access, Online International Journal Available at www.cibtech.org/sp.ed/jls/2015/02/jls.htm
2015 Vol. 5 (S2), pp. 2714-2729/Loveymi and Barati
Research Article
© Copyright 2014 | Centre for Info Bio Technology (CIBTech) 2714
OBTAINING COMPRESSIVE FLOW CURVE OF AZ41 MAGNESIUM
ALLOY REINFORCED BY 0.3 PERCENT SILICON AT HIGH
TEMPERATURE AND VARIOUS STRAIN RATES *Ali Loveymi and Farzan Barati
Department of Mechanics, Science and Research Branch, Islamic Azad University, Hamedan, Iran
*Author for Correspondence
ABSTRACT In this paper, obtaining the curve of compressive flow stress of AZ41 magnesium with0.3% silicon
additive at high temperatures and different strain rates has been considered. Also, according to this issue that the frictional behavior of a material is used in the production processes, especially the forming
processes, frictional behavior of this alloy at different deformation temperatures has been analyzed.
Compression T-shape test has been examined. The compression tests of AZ60 magnesium alloy have
been carried out at temperatures of 230 and 250°C and under the loading rates of 0.001s-1
, 0.01s-1, and
0.1s-1. Initial stress value with bending correction factor has been calculated and then using finite element
simulation with DEFORM software and multistep correction, the numerical correction factors were
obtained for each temperature and certain strain rate. The results show that, in stress-strain curves of AZ60alloy at low strains, the stress values calculated from numerical correction factor and bending
correction factor are slightly different. But with increasing the strain, the difference between the stresses
calculated from numerical correction factor is greater than bending correction factor and always the calculated stress is higher than bending correction factor. Also, the bending correction factor at all
temperatures has increased with increasing of the strain. At a constant temperature, with increasing strain
rate the maximum stress of the material is increased and at constant strain rates by increasing temperature,
the maximum stress is reduced.
Keywords: Magnesium Alloys, Compression Test, Correction Factor, Friction, T-Shape Test,
Temperature, Strain Rate
INTRODUCTION Today magnesium alloys are of interest to many researchers and have been widely used in major industries including car manufacturing and aerospace industries (Cáceres, 2009). In addition to light
weight, there are other desired characteristics in magnesium alloys such as appropriate strength that make
these alloys distinguished for other metals to be used in different industries. Some of these properties are
the ratio of strength to high weight, good fricative strength, welding capability, and recycling capability (Cáceres, 2009). Wang et al., (2011) studied the effect of adding Bi to microstructures and mechanical
properties AZ80 magnesium alloy. The results showed that with addition of Bi, hard eutectic phases are
improved and become non-continuous. Also, when the amount of Bi is greater than 1%, the amount of initial layer of Mg3 Bi2 phase increases, which splits the bed and the tensile strength and elongation
reduce. Wu et al., (2009) studied the microstructures and mechanical properties of AZ31B magnesium
alloy recycled by solid-state process from different size chips. Recycled specimens showed lower
ductility than reference ones; also, recycled samples with average surface area of the chips have the highest elongation. Grain size, the amount of oxide, and density of ingot were effective in elongation of
recycled materials Chen et al., (2011) investigated the mechanical properties and microstructures of
AZ60D magnesium alloy provided by compound extrusion. Strength and ductility of the alloy significantly improved after treatment for grain and uniform distribution between the metal particles. In
addition, the hardness of AZ41D alloy significantly increased with increasing strain from 0 to 8.240.With
increasing strain rate, the hardness slightly increases. Aghayanni et al., (2011) investigated the effects of ultrasound on the microstructure and tensile strength
of AZ60 magnesium alloy. The results showed that ultrasonic treatment of molten material before milling
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
An Open Access, Online International Journal Available at www.cibtech.org/sp.ed/jls/2015/02/jls.htm
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Research Article
© Copyright 2014 | Centre for Info Bio Technology (CIBTech) 2715
has a significant effect on the size and being spherical the α-mg dendrites, as well as the size, continuity,
and the distribution between the metal particles formed during cooling and the strength of the alloy. Liao
et al., (2011) studied the effect of thermo-electro pulsing rolling on mechanical properties and microstructure of AZ31 magnesium alloy. The results showed that WR reduces the rate of elongation
compared to raw specimen, while the TER increased this parameter. Saniei et al., (2013) studied the
behavior of compressive stress and tensile stress of AZ80 magnesium alloy. The previous pressure test should be performed at zero friction conditions, but it is impossible to provide such conditions. Therefore,
increasing correction factor and numerical correction factor are used to eliminate the effect of friction
between the surfaces. Tensile tests were carried out on standard samples at high temperatures and
different strain rates. The effect of necking phenomena was corrected using Bridgeman correction factor and was simulated using finite element software. Also, the density T-test was used to evaluate the
parameter of friction at high temperatures. Saniei et al., (2012) studied an exponential model to predict
the flow curves of several groups of AZ magnesium alloys in tension and pressure. This paper is about flow behavior of various magnesium alloys in tension and pressure such as AZ31, AZ80, and AZ81.The
tests were done at elevated temperatures and high strain rates. To eliminate the effect of heterogeneous
deformation in tension and pressure tests, the numerical method and Bridgeman method were used. A two-part mathematical model was used to predict the curves of flow stress of different magnesium alloys
in various tension and pressure. In addition, based on the proposed model, the stress was estimated at
peak state. The actual stress and strain of the necking point were estimated using a similar relationship.
Also, the behavior of the estimated flow was compatible with experimental results. Kim et al., (2010) studied a strategy for creating ultrafine-grained microstructure in magnesium alloy sheets. Li et al.,
(2013) investigated the effect of solution heat treatments on microstructure and hardness of ZK60
magnesium alloys prepared under low-frequency alternating magnetic fields. Results show that comparing with observed microstructure in the non-detection of electromagnetic field the eutectic
network structure is better found at grain boundaries under the low-frequency alternating magnetic fields
and is displayed as uniform grain distribution. Caton et al., (2002) and Mathis et al., (2002) studied the
deformation behavior of AZ41, AS21 and AE42 magnesium commercial alloys at a wide range of temperature and different strain rates. To detect the hardening and softening, they investigated and
calculated the correlation of stress to hardness strain factor. They also carried out experiments at
temperatures of 20 to 300ºC and strain rates of 0.0001s1
and showed that hardening decreases with increasing temperature and stress. Masoudpanah and Mahmoudi (2010) studied the tensile and shear
deformations and microstructure of AZ31 alloy after extrusion and ECAP. The ECAP samples comparing
with extruded samples had lower yield stress and higher tensile ductility. Zhao et al., (2010) studied in similar conditions the mechanical tensile properties and microstructure of ZK60-Y alloys that have been
produced by two different ways. Easton et al., (2010) compared deformations of magnesium alloys with
aluminum and steel alloys in terms of tension, bending, and buckling. Results showed that magnesium
alloys compared to mild steel had higher energy absorption and strength in bending and buckling. Anbuselvan et al., (2010) investigated deformation of Z60 A magnesium alloy using a pressure test. The
temperature range of the pressure test has been 300 to 500°C. Their research showed that the temperature
and strain rate are important in shaping the magnesium alloy. Furthermore, the optimal parameters in forming AZ60 magnesium alloy are the temperature of 400°C and strain rate of 0.001
s1. Sung et al.,
(2010) studied the strain rate sensitivity of the cast magnesium alloys. They examined the behavior of
three alloys of AM20, AM50 and AM60 in a wide range of strain rate, from strain rate of 0.001s-1
to 1700s
-1.Theresults showed that in low strain rates, the sensitivity to strain rate reduces with increase in
amount of aluminum alloy element in magnesium alloy. In addition, at strain rates higher than 1500s-1
,
the rate of hardness strain and strain rate sensitivity and as a result, the flow stress of the material will
greatly increase. Many studies have been done on the stress-strain relations between magnesium alloys and alloys that
have similar behaviors with these alloys, especially at high temperatures, and some models have been
proposed to predict their behaviors. Ebrahimi et al., (2006) proposed a mathematical model to show the
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
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2015 Vol. 5 (S2), pp. 2714-2729/Loveymi and Barati
Research Article
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stress-strain curves of Ti-IF steel alloys at elevated temperatures. The results of their model are in good
agreement with empirical results. Zhou et al., (1990) investigated the workability of AZ80 magnesium
alloy. They studied the compressive tests at temperature range of 200 to 500°C and strain rates of0.001s-
1to 20s
-1.
Due to friction between the contact surfaces in the pressure test, the sample becomes barreling. Several
research have been done to eliminate the effect of friction at stress-strain curve and also on barreling deformation of the specimens. Ettouney and Stelson (1983) carried out researches one deformation of the
specimen during pressure test at room temperature. They proposed a model to determine the rate of
deformation in different strains and used it to determine the friction. Narayanasamy et al., (2000)
performed a study on barreling deformation of magnesium alloys. The results showed that the radius of the barreling of the specimen has a linear relationship with geometric factor. Saniei et al., (2006) carried
out a research on pressure test and correction of strain-stress curves. Using numeral simulations, they
provided a numeral correction factor that comparing to bending correction factor has better agreement with empirical results. Bending correction factor is entirely geometrical and in which the effects of other
parameters effective in deformation process are not considered. By numerical simulation of process and
considering the effect of friction, they provided numerical correction factor. Bending correction factor always increases with increasing strain, while the numerical correction factor reduces in high strains and
with increasing the effect of friction in the process. To investigate the accuracy of their results, they
carried out the empirical tests on specimens fabricated of tin and lead at room temperature. They also
studied the effect of dimensional ratio, hardening strain exponent and strength factor in numerical correction factor.
In the present study, obtaining a compressive flow stress curve of AZ41 magnesium with0.3% silicon
additive at high temperatures and different strain rates is investigated. In previous studies, the effect of the friction factor, the ratio of height to diameter of the sample, strength
factor and the rate of hardness strain on numerical correction factor were investigated (Saniei and Fatehi,
2006).
In that study, the samples made of lead and tin were used to perform pressure testing at room temperature. Also, the experiments were performed at a constant strain rate, and strain rate sensitivity has been
assumed to be negligible. Magnesium alloys are sensitive to strain rate and forming them is done at high
temperatures. Therefore, pressure tests were conducted at two temperatures and three strain rate. Thus, investigation of
effect of strain rate and temperature in correction factor are important. So, the effects of strain rate and
temperature in correction factors were studied. The modeling of stress-strain curves of AZ60 magnesium alloys at different temperatures and strain rates is studied.
Tests to Determine the Friction Factor and Stress-strain Curve Investigation of the Effects of Parameters with Numerical Simulations
To estimate force sensitivity to friction, the sensitivity of curve slope is defined as following:
(1 )
m m=0k
m=0
K -Kλ =
K
Where, Km is the curve slope of the force with friction factor of m, and Km = 0is the curve slope of the force in condition that m=0 (conditions without friction).
Pressure Test
In this experiment, compressors with flat plates compress a cylindrical sample. The diameter changes of each step are recorded. The following relations are valid for uniform compression test.
(2 )o
o
A
A
h
hlnln
( 3 )A
P
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
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Where, Ao and A are the moment and initial section areas, h and ho are the moment and initial heights and
and are effective strain and effective stress respectively and P is the force exerted on the specimen. The Method of Bending Correction Factor
In the bending correction factor method, the flow stress of material is determined using stress analysis of
middle section of a pressurized cylindrical sample between two parallel plates. The analysis assumed that the materials are homogeneous, isotropic, and incompressible. Considering the balance condition in the
radial direction r and using geometrical conditions and plasticity equations, the following equations are
obtained using mathematical calculations (Mielnik, 1990):
(4 ))
raaR2
aR2ln()
aR2
raR2aln(
22
22
r
( 5 )
2 2
2 2
2 2[1 ln ( )] [1 ln( )]
2 2z
a aR r aR
aR aR a r
Where, is the effective stress of the material, and in Von Mayors criterion, it is calculated from following equation:
(6 )
2/12z
2r
2rz ])()()[(
2
1
In the above equations, the different parameters are as following:
, z and r the principal stresses in the peripheral and axial and radial directions respectively, and a is middle section radius of the specimen, r is the radius of the location of the desired element and R is the
radius of curvature of the barrel lateral side of the sample. Compressive force P at each section of the sample is given by the following equation:
(7 )𝑃 = 𝑂0𝑎 Sz 2prdr = 𝑝𝑎2(𝑆𝑍 ) ave
( 8 )
)2
2(ln)2( 2
aR
RaRaP
Therefore, the material flow stress is:
(9 )
2(2 ) ln (2 /(2 ))
P
Ra a R R as
p=
- -
And the relationship between flow stress ( ) and axial average stress, i.e.( )z ave
is as following:
(10 )
12( ) [(1 ) ln (1 )]
2z ave
R a
a R
The above equation can be represented as follows:
(11 )
σ = (σz)ave C , C = 1 −2𝑅
𝑎 1𝑛(1 −
𝑎
2𝑅)
−1
)
(12 )
2 2
2 1
2 1
( )
4( )
h d dR
d d
Where, C is called bending correction factor. The value of R is the radius of curvature of the barreled
sample. This radius can be obtained based on the size of the different parts of the barreled sample. For this purpose, the following formula is used:
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The Method of Numerical Correction Factor
The method of numerical correction factor is performed with finite element simulation of pressure test
using stress-strain curve obtained from a bending correction factor in the first step of the simulation. Then by measuring the height of the sample in several stages, in order to calculate the equivalent strain and
measuring the diameter of the middle-level of the simulated sample like pressure test, by dividing the
force resulted from simulation by the middle section area of the segment, the average strain is calculated. By dividing the average stress obtained from stress-strain curve in each equivalent strain, the numbers
obtained from this division are multiplied by the experimental average stress-strain curve. The re-
simulation of this experiment using the obtained stress-strain curve, the above steps is repeated (Saniei
and Fatehi, 2006). To investigate the effect of strain rate in tests, all tests were conducted at the same average strain rate and
velocity at each stage is calculated as follows:
(13 )
0, ln( )h
t h
(14 )
0vh h
t
Where, v is the velocity, h0isthe initial height of sample and h is the height of the sample after each stage of testing. By combining the relations of strain and strain rate and eliminating t from relations, for the
velocity of performing the experiment, the final equation is obtained as follows:
Description Pressure Test Pressure test has been used to determine the flow curve for AZ60alloy.In performing the tests carried out,
the following points have been considered:
1. In each experiment, the sample has been kept for five minutes at the desired temperature.
2. The experiments were performed without lubrication. 3. The dimensional ratio of the sample has been based on the ASTM standard (height to diameter ratio
equal to 1.5).
4. The strain rate at the pressure test has been kept constant. All samples have a nominal diameter of 6mm and height of 9mm. Samples were prepared by machining.
The experiments were performed by SANTAM 150kN apparatus. In this device the upper jaw is
adjustable. To perform pressure test, at least 8 identical cylindrical specimens were turned for each curve and then each cylinder was compressed up to a certain amount at one stage, the results related to force and
geometrical deformations of the sample were measured and recorded. In order to determine the effect of
strain rate in experiments, all tests were conducted at the same average rate of strain.
The Characteristics of Samples and Templates AZ 60 magnesium alloy was prepared as cast. The cylindrical specimens with diameter of 6mm and
length of 9mm were prepared by machining. For the experimental study of the effect of the radius of the
corners of templates, a distinct template with a corner radius of 1mm was provided. To make the template, steel 1.2713 according to DIN standards was used. Each frame consists of two parts; the first
part is cylindrical with radius of 29mm that a V-shaped groove was created in it by wire cutter device.
The other part is cylindrical that its inside has been machined as much as the first part such that the first
part can be completely included in the second part. Geometrical characteristics of the template have been shown in figure 1.To investigate the effects of temperature, lubrication and friction conditions, and the
radius of corners of the template of empirical experiment is shown in Table 2. Furthermore, some
experiments were carried out at two temperatures of 230 and 250°C and at strain rates of 0.01s-1
on AZ 60 alloy and in conditions without lubricant.
Table 1: Magnesium alloy composition
Material Mg Al Zn Mn
AZ60 Bal. 9.5 0.5 0.3
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Table 2: Specifications of experiments carried out
Lubricant Fillet radius(mm) Velocity(mm/min) Temperature Material
MoS2 & Dry 1 1 230 AZ60
MoS2 & Dry 1 1 250 AZ60
Figure 1: Geometrical properties of the test templates
The Mechanical Properties of the Alloys
Mechanical properties and stress-strain behavior of the used AZ 60magnesium were obtained using
simple pressure tests. These stress-strain curves were obtained at 230 and 250°C and velocity of
1mm/min. Also at two temperatures of 230 and 250°C and at strain rates of 0.001, 0.01 and 0.1s-1
, the tests was performed on AZ60 alloy, and the results of the pressure tests have been used. Also, the bending
correction factor and the numerical correction factor have been used to eliminate the frictional effect
between surfaces in test results. In fact, the corrected results have been used in simulation. Experiments have been conducted by SANTAM 150kN.The obtained stress-strain curves are shown in Figure 3.It is
known that AZ 60 magnesium alloy has softness strain behavior. To obtain better results in the finite
element simulation, each curve has been introduced as an input to the software. ش رن نش -ک ني ت نح م
strain
0.0 0.2 0.4 0.6 0.8 1.0 1.2
stre
ss(m
pa)
100
110
120
130
140
150
160
170
180
230 'c
250 'c
Figure 3: Stress-strain curve of AZ 60 magnesium alloy
The Parameters used to Measure the Effect of Friction The sensitivity of the slope is defined as follows:
(16 )
2
2
m m MoSk
m MoS
K K
K
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Where, mKis the slope of force curve with friction factor of m and 2m MoSK is the slope of the force
curve at conditions that the lubricantMoS2 is used. To calculate the slope of the curve, according to
Figure 4, the slope of the linear part of the force curve has been used. Sensitivity to the length of the extruded section can be defined as follows:
(17 )
2
2
m m MoSH
m MoS
H H
H
Where, mHis the slope of force curve with friction factor of m and 2m MoSH is the slope of the force
curve at conditions that the lubricant MoS2 is used.
Displacement / Billet diameter
0.0 0.1 0.2 0.3 0.4 0.5 0.6
Load
(N)
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
T1 dry
T1 MoS2
Figure 4: Experimental force-displacement curve of AZ 60 magnesium alloyat temperature of
230°C
RESULTS AND DISCUSSION
Results and Analyses Results of AZ60 Alloy Pressure Tests
The pressure tests of AZ60 magnesium alloy were done at temperatures of 230 and 250°C and under the loading of 0.001s
-1, 0.01s
-1, and0.1s
-1. After each experiment, the samples were rapidly cooled within
chilled water. Then, the upper, middle, and lower diameters of the barreled specimen were measured. The
mean upper and lower diameters have been used in calculating bending radius. Then, based on the data for each curve, the radius of the middle section (a) was obtained. The equations (11) and (12) were used
to obtain the radius of bending(R) and bending correction factor respectively. Initial stress value is
obtained from bending correction factor, and then by using finite element simulation and DEFORM 2D
software and multi-stage correction, correction factors for each temperature and certain strain rate have been obtained. Figure 5 shows the different stages of deformation in the simulated sample at temperature
of 250°C and strain rate of 0.001s-1. At each simulation, the behavior of the material as a function of
temperature and strain rate and as a table has been introduced to the finite element DEFORM 2D software.
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Figure 5: Various stages of deformation of simulated sample: (a) prototype (b) after the 3mm of
deformation (c) after the 6mm of deformation
The results obtained in Tables 3 to 5 for temperature of 230°C and strain rates of 0.001s
-1, 0.01s
-1 and
0.1s-1have been provided. It is clear that in the small strains, both correction factors are approximately the
same, but with increasing the strain, the differences become greater and the numerical correction factor has desired results.
Table 3: Results of the pressure test for AZ60alloy at temperature of 230°C and strain rate of
0.001s-1
NCF BCF R (mm) Final Mid
Radius
(mm)
Final height
(mm)
Force
(N)
No.
1 1.002 336.98 3.07 8.8 2756.18 1
1 1.003 270.75 3.10 8.5 3765.89 2
1 1.005 168.44 3.14 8.1 4419.00 3
1.0001 1.009 122.04 3.27 7.7 4991.12 4
1.002 1.013 66.96 3.36 7.4 5500.75 5
1.008 1.081 10.31 3.79 5.7 5821.52 6
1.034 1.099 12.99 4.42 3.8 6936.83 7
0.989 1.147 10.13 4.78 3.0 8533.27 8
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Table 4: Results of the pressure test for AZ60 alloy at temperature of 230°C and strain rate of
0.01s-1
NCF BCF R (mm) Final Mid
Radius
(mm)
Final height
(mm)
Force
(N)
No.
1 1.003 293.14 3.12 8.8 3847.46 1
1.001 1.003 226.48 3.16 8.5 4480.38 2
1.001 1.004 182.27 3.20 8.1 4972.86 3
1.002 1.006 128.86 3.25 7.7 5513.60 4
1.005 1.015 58.69 3.35 7.4 6159.78 5
1.009 1.039 25.33 3.72 5.7 6833.13 6
1.039 1.095 13.36 4.41 3.8 86007.30 7
0.98 1.139 9.96 4.51 3.0 9444.22 8
Table 5: Results of the pressure test for AZ60alloy at temperature of 230°C and strain rate of 0. 1s-1
NCF BCF R (mm) Final Mid
Radius
(mm)
Final height
(mm)
Force
(N)
No.
1 1.002 354.34 3.07 8.8 3953.00 1
1 1.004 184.89 3.08 8.5 4855.78 2
1.001 1.005 175.33 3.18 8.1 5584.73 3
1.002 1.011 77.16 3.26 7.7 6097.95 4
1.006 1.015 56.11 3.36 7.4 6695.54 5
1.015 1.039 25.16 3.69 5.7 7817.05 6
1.042 1.096 12.73 4.21 3.8 8938.09 7
1.001 1.136 10.96 4.85 3.0 12115.26 8
Based on the results obtained, the stress-strain curves of AZ60 alloy have been extracted. In Figure 6, the curves of pressure test with bending correction factor and numerical correction factor have been drawn.
At low strains, the rate of stress calculated from numerical correction factor and bending correction factor
slightly vary. But by increasing strain, the difference of stress calculated from numerical correction factor
and that of bending correction factor becomes grater, and always the stress calculated from bending correction factor is higher. Magnesium alloys generally have fixed behavior at elevated temperature and
under pressure. After working, the initial hardness reaches maximum point, and the material suffers from
softness strain and its flow stress reduces. This softness strain is the result from changes in structure of these alloys, temperature effects, and the velocity of loading in their structures, especially dynamic re-
crystallization effect which is explained by increasing the saved thermal activating energy, and changing
the microstructures during the process of elevated temperature pressure test. Finally, the material has a stable behavior. In figure (7), the comparison between displacement-force curves obtained from the
correction factors has shown.
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Figure 6: The results of pressure tests of AZ60 alloy at temperature of 250ºC and different strain
rates
displacement (mm)
0 1 2 3 4 5 6 7
Lo
ad
(N
)
2000
4000
6000
8000
10000
12000
14000
NCF
BCF
displacement (mm)
0 1 2 3 4 5 6 7
Lo
ad
(N
)
2000
4000
6000
8000
10000
12000
NCF
BCF
(b) (a)
Figure 7: The comparison between displacement-force curves for AZ60 alloy obtained from the
correction factors: (a) at temperature of 230ºC and strain rate of 0.01s-1
, (b) at temperature of
250ºC and strain rate of 0.01s-1
The Effect of Temperature and Strain Rate in Correction Factor Strain rate and temperature are effective in material flow stress, the rate of hardening and softness strain.
Figure 8 shows the effect of strain rate in numerical correction factor at temperature of 250ºC.At each
temperature, by increasing strain rate; the numerical correction factor does not significantly change at low
strains. But, by increasing strain rate, the value of numerical correction factor increases and at lower strains, it reaches its maximum value. In other words, at intermediate strains, by increasing strain rate, the
value of correction factor decreases. But at high strain, such that it was predicted, the numeral correction
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factor is decreased that the reason of this is the increasing of friction effect in forming force. However, at
high strains, the reduction rate of numeral correction factor decreases with increasing the strain rate. In
fact, by increasing strain rate the rate of friction and its effect in forming force and deformation of the sample has reduced.
strain
0.0 0.2 0.4 0.6 0.8 1.0 1.2
NC
F
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
0.001 1/s
0.01 1/s
0.1 1/s
Figure 8: The effect of strain rate in numerical correction factor in pressure test of AZ60 alloy at
temperature of 250ºC
Figure 9 shows the effect of strain rate in bending correction factor (BCF) at temperature of 250ºC. At a
fixed temperature, by increasing strain rate, the bending correction factor does not significantly change at low strains. But, by increasing strain rate, the value of bending correction factor always increases. The
reason for this fact is the ignoring of internal friction effect in forming forces related to BCF. In fact in
this method, only the effect of geometry is considered. The strain rate and temperature are effective in friction. In numerical simulations, these effects are considered and the results are close to reality.
Figure 9: The effect of strain rate in bending correction factor in pressure test of AZ60 alloy at
temperature of 250ºC
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
An Open Access, Online International Journal Available at www.cibtech.org/sp.ed/jls/2015/02/jls.htm
2015 Vol. 5 (S2), pp. 2714-2729/Loveymi and Barati
Research Article
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The effect of temperature on the numeral correction factor has been shown in figures 10 to 12. In low
strains, intelligible changes are not seen in numeral correction factor, but by increasing the strain, the
effect of temperature becomes clear. In intermediate strains, the difference of the values of numeral correction factor increases and at more elevated temperatures, higher values of numerical correction
factor are required. As mentioned previously, the value of bending correction factor always increases and
at high strains, it creates more errors. Therefore, at high strains, the stress corrected by this method is significantly different from actual stress, and then the predicted forming force by this method is more than
actual force obtained in pressure test and the necessity of using numerical correction factor and
considering all actual conditions of pressure test is completely obvious. In higher strain rates, the effect of
temperature in numerical correction factor is higher and more sensible. The reason of this phenomenon is the increasing of friction effect on temperature and higher strain rate.
strain
0.0 0.2 0.4 0.6 0.8 1.0 1.2
NC
F
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.06
230
250
Figure 10: The effect of temperature in numerical correction factor in compression test of AZ60
alloy at strain rate of 0.001s-1
strain
0.0 0.2 0.4 0.6 0.8 1.0 1.2
NC
F
0.96
0.98
1.00
1.02
1.04
1.06
230 'c
250 'c
Figure 11: The effect of temperature in numerical correction factor in compression test of AZ60
alloy at strain rate of 0.01s-1
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
An Open Access, Online International Journal Available at www.cibtech.org/sp.ed/jls/2015/02/jls.htm
2015 Vol. 5 (S2), pp. 2714-2729/Loveymi and Barati
Research Article
© Copyright 2014 | Centre for Info Bio Technology (CIBTech) 2726
Figure 12: The effect of temperature in numerical correction factor in compression test of AZ60
alloy at strain rate of 0. 1s-1
In figures 13 to 15, the effect of temperature on the bending correction factor has been shown. According to above figures, at a fixed strain, by increasing the temperature, the higher value of correction factor has
been obtained. However, the value of bending correction factor has been continuously increased in all
temperatures by increasing the strain rate. At higher temperatures, the rate of changes of numerical correction factor was higher proportion to 1 (stress state without needing correction). In fact, in
intermediate strains, by increasing temperature, the numeral correction factor has become larger. The
value of friction factor in forming magnesium alloys always depends on strain rate and forming temperature. Bending correction factor is fully geometrical and the effect of other parameters of the
process is not considered. Hence, by varying the temperature and strain rate, the amount of created error
in bending correction factor still exists. But since the numerical correction factor considers the effect of
actual parameters of shaping, by changing the temperature and strain rate, the obtained answers from numerical correction factor are more consistent with the results of experimental tests.
Figure 13: The effect of temperature in bending correction factor in compression test of AZ60 alloy
at strain rate of 0.001s-1
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
An Open Access, Online International Journal Available at www.cibtech.org/sp.ed/jls/2015/02/jls.htm
2015 Vol. 5 (S2), pp. 2714-2729/Loveymi and Barati
Research Article
© Copyright 2014 | Centre for Info Bio Technology (CIBTech) 2727
Figure 14: The effect of temperature in bending correction factor in compression test of AZ60 alloy
at strain rate of 0.01s-1
Figure 15: The effect of temperature in bending correction factor in compression test of AZ60 alloy
at strain rate of 0. 1s-1
Conclusion In this paper, by doing pressure tests on AZ41 magnesium alloy, stress-strain behavior of these alloys at
high temperatures and different velocities of deformation have been studied. Since the frictional behavior
of a material in production processes especially forming processes is used, the frictional behavior of this
alloy in different temperatures of deformation has been analyzed. T-shape pressure test that is considered as a test to measure friction and has a close affinity with real conditions of forming processes such as
forging and extrusion has been studied. Compression tests of AZ60 magnesium alloy at temperatures of
230 and 250°C and under the loading rates of 0.001s-1
,0.01s-1
, and 0.1s-1
have been performed. After performing each test, the samples have been rapidly cooled in chilled water. The initial value of stress has
been calculated with bending correction factor and then by finite element simulation with DEFORM
software and multistage correction, the numerical correction factors for each temperature and fixed strain rate were obtained. At each simulation, the behavior of the material as a function of temperature and
strain rate and in the form of tables is presented that the following results were obtained:
1. The bending correction factor always increases with increasing strain, while the numerical correction
factor reduces in high strains and by increasing the effect of friction in the process. 2. In stress-strain curves of AZ60 alloy in low strains stress, the values of stress calculated from
numerical correction factor and bending correction factor have very little difference; but by increasing the
Indian Journal of Fundamental and Applied Life Sciences ISSN: 2231– 6345 (Online)
An Open Access, Online International Journal Available at www.cibtech.org/sp.ed/jls/2015/02/jls.htm
2015 Vol. 5 (S2), pp. 2714-2729/Loveymi and Barati
Research Article
© Copyright 2014 | Centre for Info Bio Technology (CIBTech) 2728
strain, the difference of stress calculated from numerical correction factor and that of bending correction
factor becomes more and always the calculated stress is higher than bending correction factor.
3. The total changes in the correction factors at all cases are the same, and do not depend to type of material. In other words, in AZ60 alloy, bending correction factor increases with increasing strain; and in
high strains, the numerical correction factor decreases after increasing.
4. At a specified temperature, with increasing the strain rate, at low strains, the value of bending correction factor is not significantly different; but with increasing strain, the value of bending correction
factor always increases.
5. Bending correction factor at all temperatures has continuously increased with increasing strain.
6. In compression test, the material maximum stress is sensitive to strain rate and forming temperature. At a constant temperature, with increasing strain rate, the material maximum stress increases and at fixed
strain rate with increasing temperature, the maximum stress reduces.
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